Dynamic Large Deviations: In search of matching bounds

We discuss the dynamical large deviations of three models: Kac’s model of the Boltzmann Equation, a rescaled zero-range process converging to the porous medium equation, and the Landau-Lifschitz-Navier-Stokes equations. For these models, we discuss the challenges and successes of finding matching bounds, the links to well- or ill-posedness in low regularity classes, and the connection to the equality case of classical inequalities.